Joint Seminar on Quantum Information and Technologies

Quantum metrology offers an enhanced performance in experiments suchas gravitational wave-detection, magnetometry and atomic clocksfrequency calibration. Under the idealistic assumption of nodecoherence, it allows for an improvement of measurement precisionover classical protocols that grows without restraint with the numberof particles involved. Motivated by practical applications, we proposetools for quantifying the attainable quantum enhancement based on thegeometry of quantum channels and semi-definite programming thataccount for the inevitable impact of the noise. As a result we obtaina simple and direct methods yielding bounds that interpolate betweenthe quantum enhanced scaling characteristic for small number ofparticles and the asymptotic regime, in which quantum enhancementamounts to a constant factor improvement. Lastly, we are able topropose a noise model, motivated by the quantum magnetometry setups,that allows for the asymptotic constant to be arbitrarily enlarged andhence, when one is able to fully control the Hamiltonian part of thesystem evolution, the scaling enhancement to be retrieved despite thepresence of decoherence.